When something is cyclic, where the cycle "starts" is not really very relevant. What continues to matter is the relationship of steps to music.

For an international rumba, the forward or backward step (in situations where there is only one) is on the 2nd beat.

Contrastingly, in American style the forward or backward step would be on the 1st or 3rd beat (there are two traditions). Additionally, the pattern of steps would often be different from in international style, the tempo would likely be a litte faster, and the character of the music would ideally have a different flavor.